Finite Group Databasebeta

← #11995080

Subgroups — #11995080

Order 1280.

692 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#382C211yesmaximal, characteristic, complemented
2#10613811C211yesmaximal, characteristic
3#10602324C211yesmaximal, characteristic, complemented
4C2×#64671C212yesmaximal
5#10598103C212yesmaximal, complemented
6C22×C5×C4⋊C4—21no—
7C22×C42×C5C2211yescharacteristic
8C2×#4076C2211yescharacteristic
9C2×#4075—21no—
10C5×#382—24no—
11C2×C5×#95—21no—
12C2×C5×#95C2212yes—
13#65502—21no—
14#65501C2211yescharacteristic
15C2×C22⋊#168C2212yes—
16#65229—22no—
17#65228C412yescomplemented
18#65217C412yescomplemented
19#64744—22no—
20#64671—24no—
21#9156—51nomaximal, Sylow
22C23×C4×C5—22no—
23C23×C4×C5D411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5C2311yescharacteristic
26C22×C22⋊D5—21no—
27C22×D20C2×C411yescharacteristic
28C2×C5×C4⋊C4—24no—
29C2×C5×C4⋊C4—42no—
30C2×C5×C4⋊C4—42no—
31C2×C42×C5—22no—
32C2×C42×C5—22no—
33C2×C42×C5C2×C412yes—
34C2×C42×C5D412yes—
35C2×C22⋊Dic5—21no—
36#4076—22no—
37#4076—22no—
38#4075—42no—
39#4075—42no—
40C2×#685—22no—
41C2×#685—22no—
42C2×#685—21no—
43C2×C4⋊Dic5C2×C411yescharacteristic
44C2×C4⋊Dic5C2×C412yes—
45C2×#683—22no—
46C22×#168—22no—
47C5×#95—24no—
48C5×#95—22no—
49C5×#95D414yes—
50#3963—22no—
51#3963—21no—
52C22⋊#168—22no—
53C22⋊#168—22no—
54#2854—51no—
55C2×#382D511yescharacteristic, complemented
56#1817—51no—
57C2×#327—52no—
58#1294—52no—
59C24×C5C2×D411yescharacteristic
60C23×D5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—24no—
68C22×C4×C5—42no—
69C22×C4×C5—42no—
70C22×C4×C5—44no—
71C22×C4×C5—44no—
72C22×C4×C5—42no—
73C22×C4×C5—42no—
74C22×C4×C5C22⋊C412yes—
75C22×C4×C5C22⋊C412yes—
76C22×C4×C5D812yes—
77C22×C4×C5SD1612yes—
78C22×C4×C5C22×C411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5C2×D412yes—
81C22×C4×C5#4112yes—
82C2×C22⋊D5—41no—
83C2×C22⋊D5—41no—
84C2×C22⋊D5—41no—
85C2×C22⋊D5—41no—
86C2×C22⋊D5—41no—
87C2×C22⋊D5—41no—
88C22×Dic5—22no—
89C22×Dic5—21no—
90C2×D20—22no—
91C2×D20—42no—
92C5×C4⋊C4—48no—
93C42×C5—24no—
94C42×C5—24no—
95C22⋊Dic5—41no—
96C22⋊Dic5—41no—
97#685—44no—
98#685—44no—
99#685—42no—
100C4⋊Dic5—22no—
101C4⋊Dic5—42no—
102#683—44no—
103C2×#168—44no—
104C2×#168—42no—
105C2×#123—101no—
106C2×#121—51no—
107C22×C4⋊C4—21no—
108C22×C42C2×D511yescharacteristic
109C2×C22⋊C8—52no—
110#390—52no—
111#389—52no—
112#388—102no—
113#386—101no—
114#382—24no—
115#380—51no—
116C2×#95—21no—
117C2×#95C2×D512yes—
118#336—102no—
119#327—104no—
120C23×C5—22no—
121C23×C5—22no—
122C23×C5C2×C22⋊C411yescharacteristic
123C23×C5#12011yescharacteristic
124C23×C5#12311yescharacteristic
125C23×C5C2×D811yescharacteristic
126C23×C5C2×SD1611yescharacteristic
127C23×C5AGL(1,ℤ/8)11yescharacteristic
128C23×C5#13711yescharacteristic
129C22×D5—41no—
130C22×D5—42no—
131C22×D5—41no—
132C22×D5—41no—
133C22×D5—42no—
134C2×C4×C5—22no—
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—22no—
138C2×C4×C5—22no—
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5—22no—
142C2×C4×C5—22no—
143C2×C4×C5—22no—
144C2×C4×C5—22no—
145C2×C4×C5—42no—
146C2×C4×C5—42no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—44no—
150C2×C4×C5—44no—
151C2×C4×C5—44no—
152C2×C4×C5—84no—
153C2×C4×C5—84no—
154C2×C4×C5#10214yes—
155C2×C4×C5C4×D412yes—
156C2×C4×C5#12112yes—
157C22⋊D5—81no—
158C22⋊D5—81no—
159C22⋊D5—81no—
160C22⋊D5—81no—
161C2×Dic5—41no—
162C2×Dic5—42no—
163C2×Dic5—41no—
164C2×Dic5—42no—
165C2×Dic5—41no—
166C2×Dic5—42no—
167D20—82no—
168#168—82no—
169C22×D4—51no—
170C22×D4—101no—
171C23×C4—22no—
172C23×C4C22⋊D511yescharacteristic
173C23×C4C22⋊D511yescharacteristic
174C23×C4C22×D511yescharacteristic
175C22×C8—102no—
176#123—202no—
177#123—202no—
178#121—102no—
179#121—102no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—51no—
184C2×C4⋊C4—52no—
185C2×C4⋊C4—102no—
186C2×C22⋊C4—101no—
187C2×C22⋊C4—102no—
188C2×C22⋊C4—102no—
189C2×C22⋊C4—101no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42C4×D512yes—
193C2×C42D2012yes—
194C22⋊C8—102no—
195C22⋊C8—102no—
196#95—24no—
197#95—22no—
198#95—102no—
199#95—101no—
200#95C22⋊D514yes—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—22no—
206C22×C5—22no—
207C22×C5—22no—
208C22×C5—22no—
209C22×C5#38611yescharacteristic
210C22×C5#41012yes—
211C22×C5C2×#10211yescharacteristic
212C22×C5#41711yescharacteristic
213C22×C5#42112yes—
214C22×C5#44711yescharacteristic
215C22×C5#44811yescharacteristic
216C22×C5#48011yescharacteristic
217C22×C5#48111yescharacteristic
218C2×D5—81no—
219C2×D5—81no—
220C2×D5—81no—
221C2×D5—82no—
222C2×D5—82no—
223C4×C5—24no—
224C4×C5—22no—
225C4×C5—22no—
226C4×C5—42no—
227C4×C5—84no—
228Dic5—81no—
229Dic5—82no—
230C24—101no—
231C24C2×C22⋊D511yescharacteristic
232C2×D4—102no—
233C2×D4—202no—
234C2×D4—201no—
235C2×D4—201no—
236C2×D4—201no—
237C2×D4—201no—
238C2×D4—201no—
239C2×D4—201no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—24no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—102no—
254C22×C4—101no—
255C22×C4#68512yes—
256C22×C4#68512yes—
257C22×C4#68612yes—
258C22×C4#68812yes—
259C22×C4C2×C4×D511yescharacteristic
260C22×C4C2×D2011yescharacteristic
261C22×C4#70912yes—
262C22×C4C2×C22⋊D512yes—
263C2×C8—204no—
264C2×C8—202no—
265C4⋊C4—48no—
266C4⋊C4—102no—
267C4⋊C4—202no—
268C4⋊C4—204no—
269C22⋊C4—204no—
270C22⋊C4—201no—
271C22⋊C4—201no—
272C22⋊C4—204no—
273C22⋊C4—202no—
274C42—24no—
275C42—24no—
276C2×C5—21no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—21no—
280C2×C5#151212yes—
281C2×C5#151712yes—
282C2×C5#187411yescharacteristic
283C2×C5#189711yescharacteristic
284C2×C5#189911yescharacteristic
285D5—161no—
286C23—22no—
287C23—22no—
288C23—202no—
289C23—202no—
290C23—201no—
291C23—201no—
292C23—201no—
293C23C2×#68511yescharacteristic
294C23#407511yescharacteristic
295C23C2×#68611yescharacteristic
296C23#407811yescharacteristic
297C23C2×#68811yescharacteristic
298C23#408811yescharacteristic
299C23#409911yescharacteristic
300D4—402no—
301D4—401no—
302D4—401no—
303D4—401no—
304D4—401no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—84no—
324C2×C4—84no—
325C2×C4—202no—
326C2×C4—202no—
327C2×C4—201no—
328C2×C4—202no—
329C2×C4—201no—
330C2×C4—201no—
331C2×C4#394114yes—
332C2×C4C4×C22⋊D512yes—
333C2×C4#407612yes—
334C8—402no—
335C5#915611yescharacteristic, complemented, Sylow
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—401no—
345C22—401no—
346C22—402no—
347C22—402no—
348C22—401no—
349C22C2×#394111yescharacteristic
350C22#6525511yescharacteristic
351C22#6525611yescharacteristic
352C22#6525711yescharacteristic
353C22#6529412yes—
354C22#6529512yes—
355C22#6550211yescharacteristic
356C22#6550611yescharacteristic
357C22#6551611yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—84no—
363C4—401no—
364C4—402no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—801no—
370C2#1060033712yes—
371C2#1060033812yes—
372C2#1060235311yescharacteristic
373C2#1060238411yescharacteristic
374C2#1060238811yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#382C2
socleC23×C5C2×C22⋊C4
prime radicalC2×#4076C22
cosocleC23×C4×C5C23
hypercenterC2×#382D5
hypocenterC5#9156
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C5×#382C2semidirect
3. #10602324C2semidirect
5. #10598103C2semidirect
17. #65228C4semidirect
18. #65217C4semidirect
55. C2×#382D5semidirect
335. C5#9156semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C5×#3822
#106138112
#106023242
C2×#646712
#105981032
#91565